Abstract: Conventional elastic solutions cannot explain the deformation characteristic of soft rock tunnels with creep characteristics. Therefore, a Buegers model is introduced to demonstrate the space time effects in the soft rock tunnel construction period. The influence of different factors on the longitudinal deformation rule of viscoelastic rock and the spatiotemporal evolution rule have been revealed through numerical simulations. At the same time, an empirical formula for the displacement release coefficient was obtained based on the response surface method. The feasibility of the proposed method was verified by comparing it with on-site monitoring and other theoretical results. The research results indicate that the influence of geostress on the displacement release coefficient can be ignored. The Kelvin shear modulus, viscosity coefficient, Maxwell shear modulus, and excavation speed significantly affect the displacement release coefficient. According to the difference in viscosity time, it can be divided into three categories: low, medium, and high hysteresis coefficient. Empirical formulas were fitted for the longitudinal deformation curve, including time, spatial, and spatiotemporal. The research conclusion can provide a more convenient method for predicting the deformation of soft rock tunnels.

Key words: viscoelasticity, longitudinal deformation profile, soft rock tunnel, time-space effect, displacement release coefficient